Extending monotone seminorms on partially ordered vector spaces (Q1279707)

Let \(E\) be a partially ordered vector space, \(E_0\) be a majorizing subspace of \(E\), and \(p\) be a monotone seminorm on \(E_0\), that is, \(p(u)\leq p(v)\) provided \(u,v\in E^+_0\) and \(u\leq v\). The author finds a necessary and sufficient condition under which \(p\) admits a monotone extension to \(E\). The uniqueness of this extension and its completeness are discussed. There are also several interesting examples illustrating the results obtained.